This invention relates to digital signal processing systems, and is more particularly concerned with the elimination of deadband effects inherent in digital recursive filters caused by rounding of the quantization of products within the filter.
The problem of rounding errors in certain digital signal processing systems, particularly digital filtering systems, has been recognized for some time. Simply stated, rounding errors are encountered when the system is unable to detect a difference between two quantities (e.g., a voltage value) less than a finite amount which, in turn, results in a failure to reach a proper steady state, known in digital filtering parlance as "deadband". The nature of the problem is described on pages 173-174 of Introduction to Digital Filtering, R. E. Bogner and A. C. Constantinides, John Wiley & Sons, 1975, and on pages 112-116 of Digital Processing of Signals, D. Gold and C. M. Rader, McGraw-Hill Book Company, 1969. The round-off error problem is particularly acute in recursive filters, and will be better appreciated from consideration of the following specific example of a noise reduction system for color television which utilizes a recursive filter.
Commonly assigned U.S. Pat. No. 4,064,530, entitled "Noise Reduction System For Color Television", describes a system which is effective to reduce noise in a color television signal, even in the presence of significant motion between successive frames. The system includes a delay or storage device capable of storing a single television frame and a summing device for adding a fractional amplitude portion of the stored signal to a fractional amplitude portion of the present, or incoming video signal. It functions as a recursive filter and is operative automatically to change the fractional amplitude portion of the stored signal fed back to the summing device as a function of the difference between stored and present signals, thereby to change the integration time constant of the filter so as to accommodate a certain amount of motion between the arriving signal and the stored frames. The system includes a motion evaluation subsystem for detecting motion between stored frames and the incoming signal as the picture proceeds element-by-element through the system, and in response to the evaluation of such motion alters the contribution of the stored past signals to the noise-reduced video output signal. If a picture element from the same scene object in the stored past signals is sufficiently different in amplitude from the same element in the arriving video signal, the past history of that picture is ignored and only the present signal is transmitted to the output terminal; in this case, there would be no signal-to-noise improvement for that particular picture element.
That the described system when implemented in the digital domain is inherently subject to deadband will be evident from closer analysis of the operation of the system with reference to FIG. 1, which is similar to FIG. 1 of the aforementioned patent. Assuming implementation of the system for the NTSC system of color television, a PCM-encoded video input signal on input line 10 is applied via a variable attentuator 12 to one input terminal of an adding or summing circuit 14. The output signal from summer 14 is applied to a delay device 16 having a delay of (525H-.tau.); H represents one television line interval, which means that the delay device, plus miscellaneous delay .tau. in the recirculating loop including the delay device, introduce a one-frame delay, since there are 525 lines per frame in the NTSC system. The output of the delay device is applied via a second variable attenuator 18 to a second input terminal of the summer 14. Attenuators 12 and 18, shown very schematically in FIG. 1, are ganged and respectively introduce a transmission constant of (1-a) and "a"; that is, a fractional portion (1-a) of the amplitude of the arriving video signal is applied as one input to summer 14 and a fractional portion "a" of the amplitude of a stored video signal from delay device 16 is applied to the other summer input. If the value of "a" is increased, the proportion of the stored signal applied to the summer increases and the proportion of arriving video signal applied to the summer decreases. Conversely, if "a" is decreased, a larger proportion of the arriving signal and a smaller proportion of the stored signal are applied to the summer.
Although in FIG. 1 the proportions in which the incoming and stored video signals are summed are complementary with respect to unity to preserve signal amplitude normalization, the system is not necessarily implemented in this way. For example, if the arriving signal is designated x, the signal from delay device 16 is designated y, and the noise-reduced video output signal at the output of summer 14 is designated x', it will be seen that the basic equation of the system is: EQU x'=ay=(l-a)x Eq.(1)
which by very simple manipulation transforms to EQU x'=y+(l-a)(x-y) Eq.(2)
It will be noted that Equation (2) expresses the noise-reduced video output signal in terms of the input and stored video signals, one of the terms of which is the quantity (x-y), which is the difference between the arriving and stored video. It will also be noted that the right hand side of the equation requires multiplication of two terms, which for ease of digital implementation may be treated as a division of (x-y) by the reciprocal of (l-a); it is axiomatic that rounding errors are introduced whenever division occurs in digital systems.
It will be realized that Equation (2), derived from Equation (1), represents the amplitude normalized form of first-order recursive filter shown in FIG. 1. However, in an alternate form of recursive filter, for example filters of the kind described in the aforementioned text books, the input signal is not multiplied by (l-a); these are a non-normalized form in which for an input level x, the output level y can reach a magnitude of Mx or x divided by (l-a). This is the usual integrator form employed in digital recursive filtering where there may not be a serious amplitude bound as there is in television. In the more usual recursive filter, the equation form is EQU x=x+ay
which becomes ##EQU1## in which case ##EQU2## is "forced" to become zero.
The deadband inherent in a recursive filter operating according to Equation (2) will be apparent from the following Table I, which for clarity has been set forth in decimal fashion rather than binary. In Table I, "a" has been assigned a value of 0.9, from which it follows that (l-a) equals 0.1, and further it is assumed that the value of x goes abruptly to zero at T=1 following a sustained period of x=10 up to and including T=0. In other words, at T=0 x and y are both stabilized at a value of 10, and then at T=1 the value of x undergoes a step function, decreasing in value from 10 to zero.
TABLE I ______________________________________ X' = y + (1 - a) (x - y); a = 0.9, (1 - a) = 0.1 0.1 (x - y) T x y (x - y) 0.1 (x - y) rounded X' ______________________________________ 0 10 10 0 0 0 10 1 0 10 -10 -1.0 -1 9 2 0 9 -9 -.9 -1 8 3 0 8 -8 -.8 -1 7 4 0 7 -7 -.7 -1 6 5 0 6 -6 -.6 -1 5 6 0 5 -5 -.5 -1 4 7 0 4 -4 -.4 0 4 8 0 4 -4 -.4 0 4 9 0 4 -4 -.4 0 4 10 0 4 -4 -.4 0 4 11 0 4 -4 -.4 0 4 12 0 4 -4 -.4 0 4 13 0 4 -4 -.4 0 4 ______________________________________
It will be seen that the column headings from left to right are T(time), x(the amplitude of the incoming signal), y(the amplitude of the stored signal), (x-y) (the difference signal), 0.1(x-y) 0.1(x-y)rounded (which by the usual definition is rounding to the nearest integer), and x' (the output signal). By definition, the value of y (which may also be designated an output signal) in each row is the value of x' in the row earlier. Examination of this Table and the curve shown in FIG. 2 will reveal that instead of the x' output signal decaying to zero as the x signal has done, it "deadbands" at a value of four as a consequence of rounding to the nearest integer the product of the multiplication 0.1(x-y).
Although decimal numbers have been employed in Table I to illustrate the point, the same effect occurs in a PCM-encoded system employing multi-bit words. For example, if in an 8-bit encoded system it is desired to divide an 8-bit word by eight, one merely drops the three least significant bits of the word, and if the quotient is to be rounded, if the third least significant bit is a "1" it is added to the fourth least significant bit being retained; if the third least significant bit is a zero it is ignored. Basically, the process is the same as in the decimal system; if the quantity has a value of half or greater, it is rounded to the next higher integer, and if it is less than half it is ignored, thus producing the same deadband phenomena as shown in Table I.
In the noise reducing system of U.S. Pat. No. 4,064,530, deadband due to rounding causes artifacts to appear in the displayed television image, known in the art as the "ground glass" effect. This is caused by small quantizing noise effects which, because they are below the threshold of detectability of the apparatus employed in measuring the difference between the incoming and stored video signals, become "frozen" in the recirculating signal. In other words, because of the nature of the operation of digital recursive filters, small quantizing noise disturbances are literally undetectable mathematically making it impossible for them to decay to zero, or to be changed to some new value for that matter. This effect has nothing to do with the noise-reducing function of the patented system; it is inherent in any digital filter operating in the recursive mode.
It is a primary object of the present invention to eliminate deadband effects in digital recursive filters. A more specific object is to provide an improved digital noise reducing system for color television by eliminating deadband in a system utilizing a recursive filter for noise reduction.